This book is devoted to the study of a class of optimal control problems
arising in mathematical economics, related to the
Robinson-Solow-Srinivasan (RSS) model. It will be useful for researches
interested in the turnpike theory, infinite horizon optimal control and
their applications, and mathematical economists. The RSS is a well-known
model of economic dynamics that was introduced in the 1960s and as many
other models of economic dynamics, the RSS model is determined by an
objective function (a utility function) and a set-valued mapping (a
technology map). The set-valued map generates a dynamical system whose
trajectories are under consideration and the objective function
determines an optimality criterion. The goal is to find optimal
trajectories of the dynamical system, using the optimality criterion.
Chapter 1 discusses turnpike properties for some classes of discrete
time optimal control problems. Chapter 2 present the description of the
RSS model and discuss its basic properties. Infinite horizon optimal
control problems, related to the RSS model are studied in Chapter 3.
Turnpike properties for the RSS model are analyzed in Chapter 4. Chapter
5 studies infinite horizon optimal control problems related to the RSS
model with a nonconcave utility function. Chapter 6 focuses on infinite
horizon optimal control problems with nonautonomous optimality
criterions. Chapter 7 contains turnpike results for a class of
discrete-time optimal control problems. Chapter 8 discusses the RSS
model and compares different optimality criterions. Chapter 9 is devoted
to the study of the turnpike properties for the RSS model. In Chapter 10
the one-dimensional autonomous RSS model is considered and the
continuous time RSS model is studied in Chapter 11.
